A brief explanation of this may be of use as far as the limits of these pages will admit. It would be impossible to teach, by a mere description of methods, how to commence and finish off a speculum of good quality, even if every working secret and minute detail were unreservedly explained. The only way is to master sufficient theory, and the rest will come by prolonged care and perseverance. I state this because amateurs who have been desirous of enjoying the gratification of observing with a mirror of their own making have written for information which they have been quite willing even to pay for liberally, but have felt disappointed, and perhaps thought it somewhat discourteous, on being told that what they wanted was impracticable and could not be satisfactorily attempted by the Optician in writing. In some cases I have finished amateurs’ work on agreeable terms, and which has led to a pleasant correspondence or acquaintance. These remarks may prevent some future disappointment.
Every one is familiar with the fact that the parabola is the only concave surface that can reflect rays of light falling on its surface from an object at an infinite distance—such as the stars and planets practically are—to one common focus, or without aberration. This series or column of rays (which is equal in diameter to the opening of the speculum), reach the mirror without making an angle to it or to each other, they travel side by side, they are all of one length, and are reflected to a point, and are therefore all of the same length at the proper focal distance, viz., half the radius of the curvature of the concave. The properties of the parobola make the nearest possible approach to it of the utmost importance.
It has been said that a considerably under-corrected surface, if of a true and uniform curve, is better than one with less aberration, with zones or sections of various curves. To explain this, let us suppose an artificial star at some short distance, say 50 yards, the parabola would not form an image of this at the eye-piece without aberration; it has for this distance too short a focus for the central rays, and the best disc is inclined to the inner focus, because the rays from the object diverge towards it, instead of travelling parallel; and they reach the surface (the central rays compared with the marginal), at an angle equal to the semi-diameter of the mirror.
But, if instead of a parabolic mirror an elliptical one be used, which has one of its foci at 50 yards’ distance, the image will be perfect. Now place the artificial star at 500 yards, the image will now be attended with perceptible aberration. The longer focus of the ellipse must be worked further and further from the mirror by shortening the focus of the central rays. Correct it for this distance, and again remove the artificial star to a still greater distance, repeating the corrections as before and carrying the outer focus towards the object, and the inner towards the mirror, until the rays from the object become more and more parallel, and the curve is nearer and nearer to the parabola, or that eccentricity of ellipse which acts better and better for distant objects or parallel rays.
It is evident from this that if the ellipse is corrected very considerably towards the parabola, without irregularities, and every part of the surface corrected regularly from the centre to the edge (no part hastening more than another), that such a surface, though under-corrected, is much better than if one portion is fully and another under-corrected, especially if the more imperfect portion is towards the edge. Such a compound correction may show little or no outstanding aberration at the focal point, but the rays do not find a focus at the same regular pace as they would from a regular curve—one edge of a zone will be coming into focus when another would be going out. With the focussing screw they are focussed to the place where they appear to collapse, and are most satisfactory, though, in reality, the rays at the best place bend over each other, and the definition is imperfect. From a star, which is only a point, this may be more tolerated, but on the planets, where the image has a sensible diameter, and is perhaps magnified many times, this imperfect curve is very inferior to the regular one, whose error is all of one kind. The light is all there somewhere, but not with any good effect. There is no proper illumination or definition, as rays are employed which are crossing the optical axis at varying angles, and the result is confusion.
So the amateur who sets himself the pleasant task of making his own speculum (for there are many who can better afford the labour than the capital to purchase, and whose capabilities are thus superior to their means), need not be discouraged and give up the pursuit because he cannot obtain the best results by getting a perfectly parabolic glass. But if he has been successful in removing a considerable amount of the spherical error, and advanced to the elongated ellipse by maintaining a truthful curve, “let well alone” with this disc, and proceed no further, but commence another, taking care not to alter the first until the second is better, and then an improvement of the first may be attempted.
In the second attempt, should the amateur lose control over the regularity of the surface, let him try it as an experiment against the first on the planets, and he will not fail to appreciate the difference, and will be stimulated by fresh courage to get as near to the parabola as possible with the same accurate curve.
To produce a true and uniform curve is, however, the acme of troubles, whether it is desired to obtain the spherical, or parabola, or any other curve. It is generally supposed that the spherical curve is a very easy matter, so easy indeed that it is difficult to avoid. This is a very great mistake—a spherical curve of undeviating truth is as difficult a problem as a true parabola. The spherical curve is the only uniform curve, it has but one focus, and the polisher must coincide with, and be of the same radius as the glass, at every instant. This is why the optician strives to obtain a semi-polish with the grinder to lessen the risk of losing his curve on the polisher, for the curves of an object glass are spherical. The curve most liable to be obtained by the amateur is the spheroidal, a curve with its marginal rays shorter than the central, or half the radius of curvature.
There are no means with the telescope of telling the spheroidal, approximating to the sphere, from the sphere. There are no means of analyzing the exact character of a curve equal to certain methods at the centre of the curvature, but to accomplish this requires much practice and observation, with “surroundings” perfectly free from vibration. If the amateur can overcome this, and lives in or very near a town, he should only work at the polishing and figuring during the late hours of the night, when traffic, &c. have subsided. Then, by carefully preventing any draughts in the apartment, and with the mirror of the same temperature as the air in the room, he will then be able to see how varied and numerous are the chances of error in working a mirror, and the great care necessary to avoid or cure them. He will find the surface exceedingly prone to receive zones and irregularities during work, and much more so than to “work true.”
The necessity for avoiding incautious handling or heating may be realized by the following little experiment when one can manage and understand it:—Place the tip of one finger on the surface, as it hangs in the dark room ready for testing, and with very gentle pressure let it remain long enough to spell one’s name; it will then be seen that the feeble heat of the finger has, by expansion, raised a mound on the surface of the glass, and though this amount of swelling must be very small, yet it is enough to cast a shadow across the surface, as if something were laid on it, and quite ten minutes will elapse before the heat will leave this spot and the surface again become level. Now if the polisher were placed on the glass while this hillock was there, a permanent hollow would be the result. For a full account of these methods (of which Foucault was the discoverer) the reader is referred to Sir John Herschel’s and Dr. Draper’s works on the telescope.